Problem: Simplify the following expression: $ z = \dfrac{10x - 2}{5x + 2} + \dfrac{2}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{10x - 2}{5x + 2} \times \dfrac{7}{7} = \dfrac{70x - 14}{35x + 14} $ Multiply the second expression by $\dfrac{5x + 2}{5x + 2}$ $ \dfrac{2}{7} \times \dfrac{5x + 2}{5x + 2} = \dfrac{10x + 4}{35x + 14} $ Therefore $ z = \dfrac{70x - 14}{35x + 14} + \dfrac{10x + 4}{35x + 14} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{70x - 14 + 10x + 4}{35x + 14} $ $z = \dfrac{80x - 10}{35x + 14}$